Multiply the following complex numbers: $({4-2i}) \cdot ({-5+5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({4-2i}) \cdot ({-5+5i}) = $ $ ({4} \cdot {-5}) + ({4} \cdot {5}i) + ({-2}i \cdot {-5}) + ({-2}i \cdot {5}i) $ Then simplify the terms: $ (-20) + (20i) + (10i) + (-10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (20 + 10)i - 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (20 + 10)i - (-10) $ The result is simplified: $ (-20 + 10) + (30i) = -10+30i $